Mathematics
A rain gutter is formed by bending up the sides of a 44-inch-wide rectangular me

### Question Description

(a) Find a function that models the cross-sectional area of the gutter in terms of x.

A(x) =

(b) Find the value of x that maximizes the cross-sectional area of the gutter.
x =  in

(c) What is the maximum cross-sectional area for the gutter?
in2

Okie Since i dont know how the bent is done, Its either curvy or in right angled,I am assuming that the bent is done in right angle

STEP1: EXPRESSION FOR CROSS SECTIONAL AREA

x --> The inches by which the sides are bent

Cross Sectional Area = x (44-2x) or 44x-2x^2

STEP 2; FIND THE VALUE OF X USING PARABOLA EXPRESSION

Now we have to find x. To find that lets imagine a parabola from which x can be found as

x=(-b)/2a  ----> in our expression above we have a=-2; b=44

x=(-44)/(2*-2) = 11

STEP 3; SUB THE VALUE OF X to AREA FUNCTION

Now that we know x we can find the area by substituting the value

Area = (x)(44-2x) ==>(11)(44-22)==>(11)(22)==> 242 square inches

Cornell University
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